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I am in the same boat. I get the feeling that most Calculus books are just a compilation of tips and tricks. So I am suggesting you invest time into learning real analysis proper. Right now I am learning from [1]. It follows Rudin closely and as opposed to many other analysis books meant to "better explain" stuff, it goes deep into the trenches and actually tackles the subject.

[1] https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Pr...

I think time invested into studying real analysis pays off because then you can later study measure theory, functional analysis and more advanced probability to deal with curse of dimensionality and whatnot.

edit: I started studying the book linked above starting from chapter 4 since the first 3 chapters are familiar from discrete math. Then did chapter 5, skimmed chapters 6(little linear algebra), 7, 8 (most "transition to higher math" books contain this stuff) and am currently in chapter 9.




By most books I assume you mean pretty college US text books. I have no experience with them, are they really that bad ?

My previous college calculus was far from the rigour of Rudin but also far from a cookbook flavour. Unless by 'cookbook' you mean the chain rule and differentials of standard forms. It's not that hard to teach this stuff at least it's no harder than, say, geometry. I found trigonometry far more difficult.

We were first taught limits then came differentiation of polynomials using infitesimals.Chain rule was introduced. Then we ventured into differentiation of other functions. Integration was first introduced much like riemann integrals then came integration as an inverse of differentiation.


The majority of the stuff you need from calculus for deep learning doesn't rise to the level of real analysis. Real analysis is worth doing if their are benefits to Fourier transforms on your data sets in the domain you're working in but otherwise has good payoff for studying more math rather than studying more deep learning.


Broadly speaking, I want to read books like [1]. It looks like they use quite a bit of advanced nondiscrete probability. Since I prefer books written in definition - theorem - proof format anyway, I figured I might as well get analysis out the way :)

[1]http://www.cs.cornell.edu/jeh/book%20June%2014,%202017pdf.pd... (Foundations of Data Science by Bloom/Hopcroft/Kannan)




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